How to Score a Game of Bowling How to Score a Game of Bowling Erik Rank / Stockbyte / Getty Images By Jef Goodger Updated October 04, 2016. Most bowling alleys are equipped with machines that take care of the scoring for you, but you should still know how the bowling scoring system works. Otherwise, the scores the machine gives you will seem arbitrary and confusing. Bowling-Scoring Basics One game of bowling consists of 10 frames, with a minimum score of zero and a maximum of 300. Each frame consists of two chances to knock down ten pins. Instead of “points” in football or “runs” in baseball, we use “pins” in bowling. Strikes and Spares Knocking down all ten pins on your first ball is called a strike, denoted by an X on the score sheet. If it takes two shots to knock down all ten pins, it’s called a spare, denoted by a /. Open Frames If, after two shots, at least one pin is still standing, it’s called an open frame. Whereas open frames are taken at face value, strikes and spares can be worth more—but not less—than face value.

How to Score a Strike A strike is worth 10, plus the value of your next two rolls. continue reading below our video 10 Best Teams in the History of Baseball At a minimum, your score for a frame in which you throw a strike will be 10 (10+0+0). At best, your next two shots will be strikes, and the frame will be worth 30 (10+10+10). Say you throw a strike in the first frame. Technically, you don't have a score yet. You need to throw two more balls to figure out your total score for the frame. In the second frame, you throw a 6 on your first ball and a 2 on your second ball. Your score for the first frame will be 18 (10+6+2). How to Score a Spare A spare is worth 10, plus the value of your next roll. Say you throw a spare in your first frame. Then, in your first ball of the second frame, you throw a 7. Your score for the first frame will be 17 (10+7).

The maximum score for a frame in which you get a spare is 20 (a spare followed by a strike) and the minimum is 10 (a spare followed by a gutter ball ). How to Score an Open Frame If you don't get a strike or a spare in a frame, your score is the total number of pins you knock down. If you knock down five pins on your first ball and two on your second, your score for that frame is 7. Putting Everything Together Many people understand the basics but get confused when trying to add everything up. Your total score is nothing more than the sum of each individual frame. If you treat each frame individually, it's much easier to comprehend the scoring system. Breaking Down a Sample Score Frame: 168 Frame-by-Frame Explanation 1. You threw a strike, which is 10 plus your next two shots. In this case, your next two shots (the second frame) resulted in a spare. 10+10=20. 2. You threw a spare, which is 10 plus your next shot. Your next shot (from the third frame) was a 7. The value of this frame is 17 (10+7).

Added to the first frame , you're now at 37. 3. An open frame is worth exactly the number of pins you knocked down. 7+2=9. Added to 37, you're now at 46. 4. Another spare. Adding your next shot (from the fifth frame-a strike), you get 20 (10+10). Added to 46, you're at 66. 5. A strike, followed by two more strikes. 10+10+10=30, putting you at 96. 6. A strike, followed by a strike and a 2. 10+10+2=22. You're now at 118. 7. A strike, followed by a 2 and 3. 10+2+3=15, putting your score at 133. 8. An open frame. 2+3=5. You're now at 138. 9. A spare, followed by a 7 in the tenth frame. 10+7=17, putting you at 155. 10. A spare, followed by a 3.

10+3=13, resulting in a total score of 168. The Tenth Frame In the sample score, three shots were thrown in the tenth frame. This is because of the bonuses awarded for strikes and spares. If you throw a strike on your first ball in the tenth frame, you need two more shots to determine the total value of the strike. If you throw a spare on your first two balls in the tenth frame, you need one more shot to determine the total value of the spare. This is called a fill ball . If you throw an open frame in the tenth frame, you won't get a third shot. The only reason the third shot exists is to determine the full value of a strike or spare. How To Keep Score For A Game Of Bowling The Basics of Keeping Score Even with automatic scoring, it's a good idea to know the fundamentals of keeping score in the sport of bowling. After all, you have to know how to keep score if you want to know what you need to bowl to beat your opponent for either competition or just for fun!! First, what is a game of bowling?

Some people get confused when they hear the phrases "per game" or "per game per person." A game of bowling consists of 10 frames, in which a bowler has two chances per frame to knock down all ten pins. If a bowler knocks down all ten pins in those two turns in the 10th frame, an extra bonus chance is awarded. So, when we say "per game" or "per game per person," that means each 10 full frames bowled by each person. So if two people bowl one game each (10 frames each) they have bowled a total of two games. Our Automatic Scorers can fit six people on each lane, so if each person bowls a game, six complete games have been bowled. Even though each person has bowled only one game, 60 total frames have been bowled by the group, equaling 6 games.

This is an example of one complete game: Scoring There are several symbols used when keeping score: an "X" signifies a "strike" in which all ten pins have been knocked down by the first roll of the ball in a frame; a "/" signifies a "spare" in which the remainder of the pins left standing after the first roll are knocked down on the second roll in a frame; a "-" indicates that no pins were knocked down on that roll, called a "miss"; an"F" indicates a "foul" where a part of the bowler's body went past the foul line, which marks the boundry of the approach (the part of the lane where we walk and release the ball) and the lane itself, where the oil is placed and the ball rolls towards the pins; and a "O" around a number indicates that the pins left standing after the first roll are in a formation known as a "split." Some scorers, such as ours, use an "S" in front of the number to indicate a split. Splits occur when the headpin (the foremost pin) is knocked down, and there is a gap of at least one pin between all the others left standing.

The terms "wide" and "washout" are used to define this situation except that the headpin was left standing. Sometimes, a "W" is used to indicate this situation, but that has generally gone out of use. For the most part, you keep score by adding the number of pins knocked down in each frame. Special bonuses are awarded for strikes and spares. When a strike is bowled, the bowler is awarded the score of 10 (for knocking down all ten pins), plus he gets to add the total of his next two rolls to that frame. For a spare, the bowler gets the 10, plus the total number of pins knocked down on the next roll only. In the examples above, you can see that the bowler rolled a strike in the 1st frame, so he gets 10 for that frame, plus gets to add whatever he knocks down on his next two rolls. In 2nd frame, he knocked down seven pins on his first roll, indicated by the number 7.

On his second roll, he knocked down the remaining three pins standing, so he gets a spare in that frame, and adds 10 more pins to his score in the 1st frame, indicated by the number 20. He also gets the bonus for the spare, so must wait to roll another ball before adding the score for the 2nd frame. His first roll of the 3rd frame knocks down all but one pin, so he gets to add 19 pins to his total score in the 2nd frame, making the score for two frames 39. The bowler misses the pin on his second roll, so only gets a total of 9 for the 3rd frame, and that is immediately added to the total score, which becomes 48 for the first three frames. In the 4th frame, the bowler gets another strike, so no total is added until he rolls the ball two more times. In the 5th frame, on the first roll, the ball goes into the gutter, so a miss is scored, but no total is added yet until he rolls the second ball in which he knocks down 8 of the pins.

He gets a score of 18 for the 4th frame and 8 for the 5th frame, making his total score at the halfway point 74. In the 6th frame, the bowler converts a split, then his foot crosses the foul line on the first roll of the 7th frame. Even though he knocked some pins down on that roll, an "F" is marked, and zero taken because of the violation, giving the bowler only the original total of 10 for the 6th frame, making his total score at that point 84. He knocks down 6 pins in the second roll of the 7th frame, giving him a total score of 90 through seven complete frames. In the 8th and 9th frames, the bowler gets a strike each, also called a "double." Because the bowler has yet to roll two balls following the strike in the 8th frame, no total score is made yet.

In the first ball of the 10th frame, the bowler gets another strike, making three consecutive strikes which is also called a "turkey." The bowler also gets the maximum score possible for a single frame of bowling in the 8th frame, which is 30 pins, and that is added to the 90 for a total score of 120 in eight frames. Because the bowler knocked down all ten pins in one of his two available rolls for the 10th frame, he will get a bonus third roll for that frame. He knocks down eight pins on the second roll, making his total for the 9th frame 28, which is added to his total score of 120, giving him 148 for nine frames. On the bonus ball, he only gets one of the pins left standing, so he adds the 10 for the strike on his first roll to the 8 on his second roll with the 1 of his bonus third roll for a total of 19 pins in the 10th frame.

That 19 is then added to his current total score of 148, giving the bowler a final score of 167 for the game. If the bowler didn't get a strike or spare in the 10th frame, as shown here, no bonus roll is awarded and the score would look like this (with seven pins knocked down on the first roll, and all but one knocked down on the second roll). The Perfect Game Every serious bowler aspires to bowl what is called the perfect game, as one of his or her goals. As mentioned above, the maximum score for a single frame is 30 pins -- 10 for the pins actually knocked down in that frame when a strike is rolled, plus 10 pins for the first roll that follows (which would have to be a strike), and another 10 pins for the second roll (which would also have to be a strike). Times this by the 10 frames in a game of bowling and you get the perfect game -- a 300. As you can see above, it is achieved by rolling 12 consecutive strikes in a single game.

Scoring – TalkBowling Scroll Up Scoring Ten-pin bowling has a unique scoring system that can be complex for newcomers who try to score the game themselves. Because of the various multiplier effects and bonus roles that can be attained in the game, scoring is not always intuitive. A player generally receives one point for every pin knocked down on each roll of a frame. For a pin to count, it must be knocked over entirely. If it wobbles but stays standing, or moves without being toppled over completely, it is still considered standing and a score is not awarded for that pin. If a player knocked down seven pins on their first roll and one of the remaining three pins on their second, they would have a count of eight points for that frame. The number of pins knocked down in the frame is referred to as the “pinfall”. A player who rolls a ball into the gutter or fails to knock down any pins will receive a zero for their roll. In the event that pins are left standing at the end of the frame, it is referred to as an “open frame”. The score for each frame is added up at the end of the game to give a cumulative total.

The maximum score attainable is 300 (see below), while professional level bowling starts with scores of 200. Scorecard On the bowling scorecard, each frame is divided into two boxes in which the individual score from each delivery is recorded. The cumulative score after each frame is written underneath. The pinfall for each roll must be entered into the scorecard straight after the roll, and electronic scoreboards do so automatically. However, the current total cannot always be entered until the value of strikes and spares have been decided by subsequent shots (see below for further details). If a player knocked down nine pins, they would mark down a “9”. A strike is designated in the first box of the frame by an “X”. A spare is marked down on the scorecard with a “/”. A zero is recorded with a “-“. Fouls are recorded with an “F” on the scorecard. If the first roll of a frame results in a split, then this is usually recorded on the scorecard by enclosing the pinfall in parenthesis.

For example if a player knocked down eight pins and was left with a 7-9 split on the second shot, the first box of the frame would be filled with “(8)”. See below for more information on splits. 1 120 Splits A split is the name given to the pins left standing on the second ball in a frame if the head-pin (1-pin) was knocked down on the first delivery and either of the following two conditions are true: The standing pins are separated by at least one fallen pin. For instance, if the 7-pin and 9-pin were left standing, there would be a 7-9 split. A 3-10 split is another example. At least one pin is down immediately ahead of two or more standing pins, for instance a 5-6 split. There are 459 possible split combinations in ten-pin bowling. Some of the more notable include: Baby Split: 2-7 or 3-10 Bed Posts/Goal Posts: 7-10 Christmas Tree: 2-7-10 or 3-7-10 Clothesline: Any group of four pins in a line, e.g.

1-3-6-10 Greek Church: Any split in which two pins remain standing on one side and three on the other. The 5-pin must be knocked down. Lily/Sour Apple: 5-7-10 Poison Ivy: 3-6-10 The hardest shot in bowling is generally considered to be the 7-10 split, because the two remaining pins are at the furthest possible distance apart. It is extremely difficult to deliver the ball so that it hits the outside of one pin hard enough to deflect it into the other. This is particularly so because the pins are standing at the very edge of the lane and players who miscalculate their target line by even a few centimetres will end up rolling a gutter ball Strikes If a player knocks down all ten pins on their first roll, they are awarded a strike. When a strike is achieved, a player is given ten points for the ten downed pins, plus the total of their next two rolls. For this reason, the value of a strike is not known until the end of the next frame. Player rolls a strike on ball one of frame one (ten points awarded). Player knocks over five pins on ball one of frame two (five points awarded).

Player knocks down two pins on ball two of frame two (two points awarded). Player earns an additional seven points (total from frame two) for the strike in frame one. The total pinfall for frame one is 17 (10 + 7).The total pinfall for frame two is 7 points. After two frames, the player has 24 points. 1 17 24 For larger points, players must score multiple strikes in a row. Two consecutive strikes are referred to as a “double”, while three strikes in a row are called a “triple”, or “turkey”. A perfect game (12 strikes) is referred to in the US as a “Thanksgiving Turkey”. Player rolls a strike on ball one of frame one (ten points awarded). Player rolls a strike on ball one of frame two (ten points awarded). Player rolls a 3 on ball one of frame three (three points awarded). Player receives 13 extra points for the two rolls after the first strike. Player rolls a 4 on ball two of frame three (four points awarded). Player receives seven extra points for the two rolls after the second strike.

Total pinfall for frame one is 23 points, frame two pinfall is 17 points, frame three pinfall is 7 points. After three frames, player scores 47 points. 1 40 47 If a player scored three strikes in a row, they would receive a total of 30 points for the first frame strikes. This is the largest number of points that can be scored in any one frame. Spares If a player knocks down all ten pins in a frame after two rolls, they are awarded with a spare, which earns the player ten points for the ten pins that have been knocked over as well as the score of the next ball. Player bowls a 6 on ball one of frame one (six points awarded). Player bowls a 4 on ball two of frame one (four points awarded). Player bowls a 7 on ball one of frame two (seven points awarded). Player awarded seven extra points for the roll after the spare. Player rolls a gutter ball on ball two of frame two (zero points awarded). The total pinfall for frame one is now 17 (6 + 4 + 7) while frame two is worth 7 points. After two frames, player scores 24.

1 Bowling - Bowling Rules: Players Sport & Social Group - Chicago, IL Rules and Regulations The regulations listed here are generally based around regulations set by the United States Bowling Congress and the British Tenpin Bowling Association . These rules are followed by all sanctioned leagues and events, such as tournaments. This is a Recreational Bowling league. The object to have fun, bowl well, and network with new friends. Rules of play A game of bowling consists of ten frames. In each frame, the bowler will have two chances to knock down as many pins as possible with their bowling ball. In games with more than one bowler, as is common, every bowler will take their frame in a predetermined order before the next frame begins. If a bowler is able to knock down all ten pins with their first ball, he is awarded a strike. If the bowler is able to knock down all 10 pins with the two balls of a frame, it is known as a spare. Bonus points are awarded for both of these, depending on what is scored in the next 2 balls (for a strike) or 1 ball (for a spare).

If the bowler knocks down all 10 pins in the tenth frame, the bowler is allowed to throw 3 balls for that frame. This allows for a potential of 12 strikes in a single game, and a maximum score of 300 points, a perfect game . Handicap A handicap system will be used to determine team wins and losses for standings and playoff seeding. Each individual player's handicap will be used to calculate a team total for the week. Handicaps adjust from week to week as more games are added to a player's average. The handicap is calculated by subtracting the player's average from 200 and then taking 80% of that total. This handicap is added to each player's "scratch" (actual) score to establish the totals. The handicap total is calculated after all games for the week are played and then the scores are adjusted to reflect the new total and then wins/losses are determined for the standings. Scoring In general, one point is scored for each pin that is knocked over. So if a player bowls over three pins with the first shot, then six with the second, the player would receive a total of nine points for that frame.

If a player knocks down 9 pins with the first shot, but misses with the second, the player would also score nine. When a player fails to knock down all ten pins after their second ball it is known as an open frame. In the event that all ten pins are knocked over by a player in a single frame , bonuses are awarded. A ten-pin bowling score sheet showing how a strike is scored: Strike : When all ten pins are knocked down with the first ball (called a strike and typically rendered as an “X” on a score sheet), a player is awarded ten points, plus a bonus of whatever is scored with the next two balls. In this way, the points scored for the two balls after the strike are counted twice.

Frame 1, ball 1: 10 pins (strike) Frame 2, ball 1: 3 pins Frame 2, ball 2: 6 pins The total score from these throws is: Frame one: 10 + (3 + 6) = 19 Frame two: 3 + 6 = 9 TOTAL = 28 A player who scores multiple strikes in succession would score like so: Frame 1, ball 1: 10 pins (strike) Frame 2, ball 1: 10 pins (strike) Frame 3, ball 1: 4 pins Frame 3, ball 2: 2 pins The score from these throws are: Frame one: 10 + (10 + 4) = 24 Frame two: 10 + (4 + 2) = 16 Frame three: 4 + 2 = 6 TOTAL = 46 The most points that can be scored in a single frame are 30 points (10 for the original strike, plus strikes in the two subsequent frames).

A player who bowls a strike in the tenth (final) frame is awarded two extra balls so as to allow the awarding of bonus points. If both these balls also result in strikes, a total of 30 points (10 + 10 + 10) is awarded for the frame. These bonus points do not count on their own; they only count as the bonus for the strike. A ten-pin bowling score sheet showing how a spare is scored: Spare: A “spare” is awarded when no pins are left standing after the second ball of a frame; i.e., a player uses both balls of a frame to clear all ten pins. A player achieving a spare is awarded ten points, plus a bonus of whatever is scored with the next ball (only the first ball is counted). It is typically rendered as a slash on score sheets in place of the second pin count for a frame.

Example: Frame 1, ball 1: 7 pins Frame 1, ball 2: 3 pins (spare) Frame 2, ball 1: 4 pins Frame 2, ball 2: 2 pins The total score from these throws is: Frame one: 7 + 3 + 4 (bonus) = 14 Frame two: 4 + 2 = 6 TOTAL = 20 A player who bowls a spare in the tenth (final) frame is awarded one extra ball to allow for the bonus points. The maximum score in a game of ten-pin is 300. Playoffs All teams will make the league playoffs. Teams will be seeded based on the end of season standings. Teams will advance by bowling a higher team score (pins + individual player handicaps added to each game) in the playoffs. All leagues that have 12 or more teams will be split into a Flight A & Flight B Playoff Bracket. At the end of the season all captains are responsible for confirming their team’s end of season team record. Once playoff brackets are posted and playoff games are played the tournament seeding will not be changed.

If there is an incorrect score posted for your team, the captain is responsible for notifying the league office prior to the playoffs being played. During the regular season it is ok for team captains to ask players from other teams to “Sub or Fill In” open slots on game day, to avoid forfeit. In the playoffs, a player can only participate and play for one team. If a player is found playing on two or more teams in the playoffs all games are subject to forfeit. Player Rules Teams consist of four players with no gender rule in place. Your team can have a maximum of 8 players on the roster. Teams can bowl four people (4) the first game and then bowl a new set of players the following game. The new set of players can consist of one (1) new bowler or four (4) new bowlers. Schedule & Standings Schedules and standings will be updated weekly throughout the season. Standings are determinded by cumulative pin total with individual player handicaps added to each game score. FORFEITS All About Bowling Scores ALL ABOUT BOWLING SCORES Ever wonder what the most common bowling score is?

Well, obviously this depends on the skill levels of the players involved, but what if we were to simply look at all possible games and analyze their scores? How many different ten-pin bowling games are there, and what is the most common score among them? What is the relationship between the score and the average number of strikes and spares? With a little help from the computer, we can come up with some interesting answers. For derivations, see the material further down the page. First, it seems evident that the total number of possible ten-pin bowling games is quite large. We have eleven possibilities for the first ball thrown in the first frame (gutter, 1, 2, ..., 9, strike), and the same possibilities occur for each of the other nine frames. So without even considering the second ball in each frame, at a minimum we have 11¹º = 26 billion possibilities. In fact, the true number of games is much, much larger due to the effect of the second ball in each frame.

It's easy to show that the total number of possible games is 66^9 x 241 = 5,726,805,883,325,784,576 (about 6 billion billion, or 6 quintillion) Calculations of the score distributions for these games results in the following table for the number of possible games and the associated probability if all scores were equally likely: Score Number of possible games Probability 0 1 < 0.01% 1 20 < 0.01% 2 210 < 0.01% 3 1,540 < 0.01% 4 8,855 < 0.01% 5 42,504 < 0.01% 6 177,100 < 0.01% 7 657,800 < 0.01% 8 2,220,075 < 0.01% 9 6,906,900 < 0.01% 1

0 20,030,010 < 0.01% ...

77 172,542,309,343,731,946 3 % ... 288 12 < 0.01% 289 11 < 0.01% 290 11 < 0.01% 291 1 < 0.01% 292 1 < 0.01% 293 1 < 0.01% 294 1 < 0.01% 295 1 < 0.01% 296 1 < 0.01% 297 1 < 0.01% 298 1 < 0.01% 299 1 < 0.01% 300 1 < 0.01% The full table is shown below . For each score above 290, there is only one possible way to play the game. This distribution is shown in the following diagram. It is not precisely symmetric about its maximum point.

The most common score out of all the possibilities is 77. This is the mode of the score distribution. The mean of the distribution is about 79.7, so if you score above that, you can certainly argue that you're doing better than average! If we show the cumulative probability histogram corresponding to the score distribution, we can get an idea of the percentiles for various scores: For example, if we bowl 98 or higher, we're already in the 90th percentile of all possible bowling scores. The median, or 50th percentile, of the score distribution is 79. The effect of strikes and spares on the average score can be seen in the following contour-line diagram: As expected, the average score increases with the number of strikes and spares, and the influence of strikes increases with larger scores. It's easy to see from the score contour lines in this diagram how much we can expect to increase our average score with more strikes or spares.

The information in this diagram is presented in tabular form below, along with the minimum and maximum scores possible for various quantities of strikes and spares: For example, games with two strikes and four spares average 114 points, but could be as low as 60 or as high as 162, depending on the particular balls thrown in the game. We can also compute the average number of strikes and spares in a game with a given score: The average numbers of strikes and spares per game are approximately equal for games scoring about 175. Obviously the only game with 12 strikes scores 300. The average number of balls thrown in a game is highly influenced by the number of strikes, but there are side effects resulting from the special scoring in frame 10: As low scores increase to about 90, the occasional third ball in the tenth frame increases the total number of balls thrown on the average. The maximum possible number of balls thrown in a game is 21, resulting from nine non-strike frames followed by a tenth frame with three balls.

It's possible to have a game with as few as 11 balls, but the only way would be with all strikes in the first nine frames followed by an open tenth frame. If A and B were the balls thrown in frame 10 (0 ≤ A ≤ 9, 0 ≤ A + B ≤ 9), then the score of such a game would be 240 + A + 2(A + B): Score through frame 7 210 Points earned in frame 8 20 + A Score through frame 8 230 + A Points earned in frame 9 10 + A + B Score through frame 9 240 + 2A + B Points earned in frame 10 A + B Final score 240 + 3A + 2B The final score for the 11-ball game falls in the range [240,267]. However, the average number of balls thrown for games scoring in this range is well above 11, so the effect of these relatively-unusual 11-ball games is not apparent on the chart above. Derivation of the total number of possible games.

In each of frames 1 - 9, there are 66 possible ways to score the two balls thrown (or single ball in the case of a strike). To see this, let 0 represent a gutter ball and 10 a strike. The possibilities for the first ball A are in the range 0 to 10, inclusive (0 ≤ A ≤ 10). If A is not a strike (A ≠ 10), then there are (11 - A) possibilities for the second ball B: 0 ≤ B ≤ 10 - A. Including the strike possibility, the total number of ball combinations for one frame then is 9 10-A 9 11 1 + ∑ ∑ 1 = 1 + ∑ (11-A) = 1 + ∑ A = 1 + 66 - 1 = 66 A=0 B=0 A=0 A=2 It follows that the number of possible ways to score the first nine frames is 66^9 (66 raised to the ninth power).

The number of possible outcomes for the two or three balls thrown in Frame 10 can be summarized in the following table: First ball Total 241 9 9-B 9 9-A * ∑ ∑ 1 = 55 ** ∑ ∑ 1 = 55 B=0 C=0 A=0 B=0 Since there are 241 possible ways to score the tenth frame, the result given at the top of this page for the total number of games follows. Analysis of average strikes and spares at higher scores. As we saw in the above diagram , the average number of strikes and spares exhibits locally non-monotonic behavior at higher scores, probably due to the vastly fewer number of possible games for these scores. For example, the average number of strikes in a 280-point game actually exceeds that in a game scoring 281. This result may run counter to our overall intuition that higher-scoring games should include greater numbers of strikes, but can be confirmed by enumerating the twenty-six possible 280-point games: Frame Game 1 2 3 4 5 6 7 8 9 10 Strikes 1.

X - / X X X X X X X X X X 11 2. X 1 / X X X X X X X X X X 11 3. X 2 / X X X X X X X X X X 11 4. X 3 / X X X X X X X X X X 11 5. X 4 / X X X X X X X X X X 11 6. X 5 / X X X X X X X X X X 11 7. X 6 / X X X X X X X X X X 11 8. X 7 / X X X X X X X X X X 11 9. X 8 / X X X X X X X X X X 11 10. X 9 / X X X X X X X X X X 11 11. - / X X X X X X X X X X - 10 12. 1 / X X X X X X X X X X - 10 13.

2 / X X X X X X X X X X - 10 14. 3 / X X X X X X X X X X - 10 15. 4 / X X X X X X X X X X - 10 16. 5 / X X X X X X X X X X - 10 17. 6 / X X X X X X X X X X - 10 18. 7 / X X X X X X X X X X - 10 19. 8 / X X X X X X X X X X - 10 20. 9 / X X X X X X X X X X - 10 21. X X X X X X X X X X - / 10 22. X X X X X X X X X X 1 8 10 23. X X X X X X X X X X 2 6 10 24. X X X X X X X X X X 3 4 10 25.

X X X X X X X X X X 4 2 10 26. X X X X X X X X X X 5 - 10 Total 270 and the fifteen possible 281-point games: Frame Game 1 2 3 4 5 6 7 8 9 10 Strikes 1. - / X X X X X X X X X X 1 10 2. 1 / X X X X X X X X X X 1 10 3. 2 / X X X X X X X X X X 1 10 4. 3 / X X X X X X X X X X 1 10 5. 4 / X X X X X X X X X X 1 10 6. 5 / X X X X X X X X X X 1 10 7. 6 / X X X X X X X X X X 1 10 8. 7 / X X X X X X X X X X 1 10 9.

8 / X X X X X X X X X X 1 10 10. 9 / X X X X X X X X X X 1 10 11. X X X X X X X X X X 1 9 10 12. X X X X X X X X X X 2 7 10 13. X X X X X X X X X X 3 5 10 14. X X X X X X X X X X 4 3 10 15. X X X X X X X X X X 5 1 10 Total 150 The average number of strikes in a 280-point game is 270/26 = 10.38, but the average number in a 281-point game is only 150/15 = 10. A similar type of behavior occurs with the average number of spares. The "Whale" chart.

If we plot the average, minimum and maximum score against the number of strikes and then repeat the plot for various numbers of spares, we get the following unusual diagram: This diagram is vaguely reminiscent of the head and mouth of a humpback whale, but the information it contains is probably easier to derive from the score contour line diagram . Score distribution table . Here's a full table showing the number of possible games for each score: Score Total 5726805883325784576 Computation algorithm. Obviously it isn't feasible to score all 6 quintillion possible games and enumerate the results individually. But with a "divide-and-conquer" strategy, we can derive the correct results by performing convolutions on small portions of the game. The convolution methodology is based on combining all possible types of throwing patterns from one group of frames with all possible patterns in a subsequent group of frames. The quantity stored in memory arrays is the number of games with the given combination of parameters, so the resulting convolution is formed simply by multiplying the number of games in the first group by the number of games in the second group since any game in the first group can be followed by any of the games in the second group.

The first group of frames must track four scoring possibilities forward that require knowledge of the first two balls A and B thrown in the second group of frames. These four possibilities are: 1) an open frame resulting in no extra score (0 points added); 2) a spare adding in the score from the next ball (A); 3) a strike adding in the score from the next two balls (A + B); and 4) a double strike in the last two frames adding in twice the score from the next ball as well as the score from the second ball following (2A + B). Results are kept in four separate tables for each partial score. To be properly combined in the convolution, the array in the second group is identified by all possible values for its first two balls A and B, which are tracked backward into the convolution performed with the first group of frames. To simplify programming, A and B are each allowed to range from 0 to 10 (121 total combinations) even though certain combinations of A and B are invalid (these invalid combinations will have zero entries for the number of games and are ignored in the computations).

An array of possibilities for the first three frames is computed and then convolved with itself to form results for the first six frames. This result is convolved with the array for the first three frames to produce results for the first nine frames. Finally, that result is convolved with computations for frame 10 in order to generate results corresponding to the entire game. Bowling Score Calculator | SportCalculators Contact Bowling Score Calculator How one throw effects on bowling score? What would be the score if you throw 5 and spare for each frame? Find out the answers with this bowling score calculator. data-ad-format="horizontal" CLICK HERE to become a bowling star by storing and analyzing your results! How to Use the Calculator?: Push the buttons for values for each frame throw by throw. The calculator calculates your current score after each input and enables only the buttons you are able to push. Push "X" for strike and "/" for spare. You can start a new game at any point be pressing the "new game" button. Please note that your score is not saved, so if you refresh the page, you might loose your score. Bowling Bowling is an indoor-game played usually in special bowling alleys.

The are many variations of the game but the most common one is the ten pin bowling (for the other variations see resource links in the end of the page). The gaming equipment consists of a bowling ball and ten bowling pins. Pins are placed in a triangle shaped formation in the other end of the bowling lane, which is 60 feet (~18 meters) long. The bowling ball is thrown from the other end of the line and the goal is to knock down as many pins as possible. Matches consists of games played by each player. One game consists of ten frames and each frame, except the tenth frame, consists of two throws. The tenth frame can have two or three throws depending on previous throws. Scoring a bowling game is not straightforward and that is why I made the bowling score calculator above. To understand the scoring let's take a look at the three possible endings of a frame. An open frame An open frame is when a player doesn't knock all 10 pins down in both attempts. The score of the frame is the amount of pins knocked down. Strike Strike happens when a player knocks down all 10 pins on the first throw. In this case there will be no second throw in that frame.

The score of the frame is ten points. Spare If a player knocks down all 10 pins with two throws he/she gets a spare. For example the player knocks down 3 pins on the first throw and 7 on the second (or 0 and 10 respectively). The score of the frame is ten points. How to score a bowling game? If a player makes only open frames the scoring is straightforward. In this case the result of the game is the sum of frames. Getting strikes and spares makes calculation a bit more complicated. Let's take a look at the spare first. The next throw after the spare frame affects the score of the spare frame. The amount of pins knocked down with the next throw are added to the score of the spare frame. For example: The player makes spare for the first frame. In the second frame the player throws 3 with his/hers first throw, which changes the score of the first frame to 13. The second throw of the second frame is calculated normally. So if the player throws for example 2, the total score after two frames is 18. Strike has a same kind of effect than the spare but it lasts for two throws.

If a player makes a strike on his/hers first throw and 3 and 2 in the second frame, his/hers score after the two frames is 20. This is because the 3 and 2 are added to the first frame making the score of the first frame 15. The second frame is an open frame and the score is 5. Getting strikes in a row makes the players score higher very fast. Let's say the player gets three strikes in a row. This makes the score of the first frame to be 30, which is also a maximum for a frame. And if the player throws to his/hers fourth frame 3 and 2, the bonus ends and after four frames his/hers score will be 73. Try this out with the bowling score calculator above! This calculator and article is for ten-pin-bowling. See Wikipedia for much detailed article about ten-pin-bowling and other types of bowling . If you get tired of chasing that 300 game you can also try these trickshots for a change. Enjoy!

Image courtesy of Salvatore Vuono / FreeDigitalPhotos.net Bowling Score Calculator A strike (X) is when the bowler knocked down all 10 pins on the first try. (i.e. the first ball rolled). Since it's a strike there is no need to roll the ball for a second try for that frame! A spare (/) is when the bowler knocked down less than 10 pins with the first try (the first ball rolled) but knocked down the remaining pins with the second ball for a total of 10 pins knocked down for that frame. The maximum score for a game = 300 Examples of scoring Take a simple game where you have no strikes and no spares. You just throw 2 balls per frame knocking down 5 on your first ball and 3 on your second ball. And.. by chance you do this for all 10 frames of the game. So... each frame would be worth 8 points for a grand total score of 80 for the whole game Let's hope you are a bit better than that and get a strike.

Strikes are worth more and are a little more complicated to score The rule for a strike score is as follows: The score for the strike frame = 10 plus the total of the next TWO BALLS THROWN plus the previous frame score. What?? Say you have the following scores frame #1 = 8 (you rolled two balls but only knocked down 8 pins) frame #2 = X (strike!) You knocked down all 10 pins with the first ball) frame #3 (ball 1) = 7 pins knocked down and ball 2 = (only 1 more pin knocked down) Your score for frame #1 = 8 Your score for frame #2 = 10 + frame3(ball1) + frame3(ball2) + frame #1 score = 10 + 7 + 1 + 8 = 26 (this is the score you write down in the frame #2 box) Your score for frame 3 is just simple math or frame 2 + frame 3 = 34 (the score written in frame #3 box) Remember you can't compute frame 2's score UNTIL you have thrown TWO more balls (in frame 3)!!!

Try this on the calculator and watch the scores appear. Now you get a spare Spares are almost the same as strikes except they are worth 10 points plus the value of the next ball thrown. What?? Continue with frame #4 frame #4 you roll ball 1 and knock down 5 pins so ball 1 = 5 on your second ball for Frame #4 you knock down the remaining pins ball2 = 5 (all pins knocked down - 2 balls spare!) you can't total frame 4 yet because you need the value of your next ball in upcoming frame#5 Say in frame #5 you roll your ball and knock down 8 pins on the first roll. Ball 1 in Frame # 5 = 8 Now we can determine Frame #4s score. Now frame #4 score = 10 + frame 5(ball 1 value) + the score total in frame#3 = 10 + 8 + 34 Continuing on you roll your second ball in Frame#5 and you knock down 1 more pin.

So the total score for frame #5 will be: frame #5 score = 52 (from frame#4) + 9 from frame #5 total = 61 Try this on the calculator and watch the scores appear. Another tricky part is the 10th frame if you get a strike on your FIRST ball - you must throw TWO more balls so you can compute the 10th frame score. (If these balls are strikes also, they only count as 10 each. They are just needed to get your next ball values.) You get a spare by a combination of your first and your SECOND ball you must throw a third ball to compute the spare equation. YOU ONLY THROW UP TO 3 balls in the 10th frame. Hope this helps, try it out on the calculator Close We are bowlers and we strive to make this the Internet's best bowling score calculator. Today we have a calculator for the 10 Pin bowlers out there and another calculator for Duck Pin bowlers. Of course one of the main reasons for this application is to answer the "what if's". At work the next day after league play from the previous night those missed spares nag at me.

Have you ever wondered - What if I just picked up one more spare? Well, this website is for you. Try it on on your mobile device! Please send us your feedback - bowlinggenius@bowlinggenius.com Close How to use this calculator This is a website that calculates a bowling score based upon your input. You can have as many as 12 simultaneous games on the screen at one time. Simply click the button that says <Start Another Game> If you want more games to appear then click the <Start Another Game> button again and again. Scoring This website is designed to allow you to enter valid scores only for a normal 10 Pin bowling game. It enforces the normal rules of bowling as if you were actually at the bowling ally. You must progress to enter scores from Frame #1 through Frame #10 just as you would if actually bowling in a game. The current frame you are bowling, the frame you can enter a value in, is highlighted in light blue. To enter a value in the current active frame simply click a ball score button located above indicating how many pins you knocked down. The calculator will automatically put the correct ball score value in the correct spot on the bowling sheet.

Ball 1 score appears on the left side of the frame and ball 2 score appears in the small box on the right side of the frame. Strikes appear as an X and spares appear as a / Your total score for the frame appears below the ball score values just as it does on normal scoring at the bowling ally. Total score for the game appears in the last active frame. Rescoring and Corrections Simply click with your mouse any frame to rescore the value and see what the new score for the game calculates to. This allows extremely easy what if scenarios. Max Score Possible As you enter values you will notice the Max Possible value changing. This box is intended to show you what score would be possible if you made strikes for the remaining frames left in the game. Handicap Information Click the icon in the upper left area near frame #1 and when the popup menu appears enter handicap and bowler name information for this game. Once you enter a handicap value the total handicap score should compute. The bowling games are draggable objects. Simply move the whole game with your mouse to organize your screen. Too many games appearing? Click the up arrow icon to minimize a game. A down arrow icon will appear to restore the game.

To delete a game simply click the trash can icon. Mobile devices This website has been designed to automatically scale to most devices. If it does not appear normal on your device please let us know. Errors If you find an error, we hope you do not, but Please let us know! This website has been to designed with the intent you have an connection to the Internet. If you disconnect from the Internet your current active games should continue to work but you will not be able to start new games. Offline modes are in the works. Close

Question: What is the maximum score possible in a game of ten pin bowling?
Answer: 300